Some new congruences for Andrews' singular overpartitions

JOURNAL OF NUMBER THEORY

卷:173

Article

Kathiravan, T.¹  Fathima, S. N.¹ 

[1] Pondicherry Univ, Dept Math, Ramanujan Sch Math, Pondicherry 605014, India

关键词: Singular overpartition;    Theta function;    Congruence;    Dissection;   

DOI  :  10.1016/j.jnt.2016.09.026

来源: Elsevier

【 摘 要 】

Recently, Andrews defined combinatorial objects which he called singular overpartitions and proved that these singular overpartitions which depend on two parameters k and i can be enumerated by the function (C) over bar (k,i)(n), which denotes the number of overpartitions of n in which no part is divisible by k and only parts equivalent to +/- i (mod k) may be overlined. G.E. Andrews, S.C. Chen, M. Hirschhorn, J.A. Sellars, Olivia X.M. Yao, M.S. Mahadeva Naika, D.S. Gireesh, Zakir Ahmed and N.D. Baruah noted numerous congruences modulo 2,3,4,6,12, 16, 18,32 and 64 for (C) over bar (3,1)(n). In this paper, we prove congruences modulo 128 for (C) over bar (3,1)(n), and congruences modulo 2 for (C) over bar (12,3)(n), (C) over bar (44,11)(n), (C) over bar (75,15)(n), and (C) over bar (92,23)(n). We also prove Mahadeva Naika and Gireesh's conjecture, for n >= 0, (C) over bar (3,1)(12n +11) equivalent to 0 (mod 144) is true. (C) 2016 Published by Elsevier Inc.

【 授权许可】

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